3,355 research outputs found
Longitudinal excitations in quantum antiferromagnets
By extending our recently proposed magnon-density-waves to low dimensions, we
investigate, using a microscopic many-body approach, the longitudinal
excitations of the quasi-one-dimensional (quasi-1d) and quasi-2d Heisenberg
antiferromagnetic systems on a bipartite lattice with a general spin quantum
number. We obtain the full energy spectrum of the longitudinal mode as a
function of the coupling constants in the original lattice Hamiltonian and find
that it always has a non-zero energy gap if the ground state has a long-range
order and becomes gapless for the pure isotropic 1d model. The numerical value
of the minimum gap in our approximation agrees with that of a longitudinal mode
observed in the quasi-1d antiferromagnetic compound KCuF at low
temperature. It will be interesting to compare values of the energy spectrum at
other momenta if their experimental results are available.Comment: 19 pages, 4 figure
Excited states of quantum many-body interacting systems: A variational coupled-cluster description
We extend recently proposed variational coupled-cluster method to describe
excitation states of quantum many-body interacting systems. We discuss, in
general terms, both quasiparticle excitations and quasiparticle-density-wave
excitations (collective modes). In application to quantum antiferromagnets, we
reproduce the well-known spin-wave excitations, i.e. quasiparticle magnons of
spin . In addition, we obtain new, spin-zero magnon-density-wave
excitations which has been missing in Anserson's spin-wave theory. Implications
of these new collective modes are discussed.Comment: 17 pages, 4 figure
On a property of random-oriented percolation in a quadrant
Grimmett's random-orientation percolation is formulated as follows. The
square lattice is used to generate an oriented graph such that each edge is
oriented rightwards (resp. upwards) with probability and leftwards (resp.
downwards) otherwise. We consider a variation of Grimmett's model proposed by
Hegarty, in which edges are oriented away from the origin with probability ,
and towards it with probability , which implies rotational instead of
translational symmetry. We show that both models could be considered as special
cases of random-oriented percolation in the NE-quadrant, provided that the
critical value for the latter is 1/2. As a corollary, we unconditionally obtain
a non-trivial lower bound for the critical value of Hegarty's
random-orientation model. The second part of the paper is devoted to higher
dimensions and we show that the Grimmett model percolates in any slab of height
at least 3 in .Comment: The abstract has been updated, discussion has been added to the end
of the articl
Characterizing mixed mode oscillations shaped by noise and bifurcation structure
Many neuronal systems and models display a certain class of mixed mode
oscillations (MMOs) consisting of periods of small amplitude oscillations
interspersed with spikes. Various models with different underlying mechanisms
have been proposed to generate this type of behavior. Stochastic versions of
these models can produce similarly looking time series, often with noise-driven
mechanisms different from those of the deterministic models. We present a suite
of measures which, when applied to the time series, serves to distinguish
models and classify routes to producing MMOs, such as noise-induced
oscillations or delay bifurcation. By focusing on the subthreshold
oscillations, we analyze the interspike interval density, trends in the
amplitude and a coherence measure. We develop these measures on a biophysical
model for stellate cells and a phenomenological FitzHugh-Nagumo-type model and
apply them on related models. The analysis highlights the influence of model
parameters and reset and return mechanisms in the context of a novel approach
using noise level to distinguish model types and MMO mechanisms. Ultimately, we
indicate how the suite of measures can be applied to experimental time series
to reveal the underlying dynamical structure, while exploiting either the
intrinsic noise of the system or tunable extrinsic noise.Comment: 22 page
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